Tomas Rosicky has conceded that Arsenal's Premier League title hopes are all but over while his team-mate Bacary Sagna admitted that they have been undermined by the loss of the injured Robin van Persie and urgently "need to find a solution".

The players reflected the sense of deflation inside the Arsenal dressing room as they considered the wreckage of Sunday's 3-0 home defeat to Chelsea. "It will be very difficult for us to win the title now, we know that," Rosicky said, after his team's fourth defeat of the Premier League season which has left them 11 points adrift of the leaders, Chelsea, albeit with one game in hand. "It's not easy, of course, to take this defeat but well done to Chelsea because they took their chances. If they continue to play like they did against us until the end, then it will be difficult for anyone to stop them."

Arsenal have battled a raft of injuries since the beginning of the season but Van Persie's is arguably the most demoralising. The striker was originally told the ankle ligament he damaged on international duty with Holland was partially ruptured yet further tests have revealed a complete tear. The anticipated absence of five months would rule him out of all but the final few weeks of the domestic season.

It has also led to renewed calls for the manager, Arsène Wenger, to sign fresh blood in January. Nicklas Bendtner, another of his recognised strikers, has been out since the beginning of last month with a groin injury and is not expected to return until Christmas.

"Robin's absence is weighing heavily on us," said Sagna. "We need to find a solution and we can't afford to fool ourselves. There was too much of a gap between ourselves and Chelsea. They were better than us in the individual battles, they retained possession better than we did and they passed the ball better. Chelsea swept us aside and we are very disappointed."

Wenger was asked whether Van Persie's long-term absence would prompt him to enter the transfer market in January, something he has traditionally been reluctant to do. He generally regards the winter window as a time for panic buying, although he did sign Andrey Arshavin during the previous one.

"I would rather have all our [injured] players back," Wenger replied. "I'm not in the mood now to say I will buy players. We have to deal with the disappointment [of Chelsea] and respond to that by trying to win our next game."

Wenger has little chance of signing Marouane Chamakh, the striker he chased over the summer. Bordeaux blocked Chamakh's move then and they will do so again in January. Although Chamakh is out of contract at the end of the season, Bordeaux, who are enjoying an excellent season, believe that he is worth more to them on the field for the final months of his contract. Wenger has also shown an interest in the Toulouse and France striker André‑Pierre Gignac.

Wenger has promised to field his usual blend of young hopefuls and fringe first-team members in the Carling Cup quarter-final tie at Manchester City tomorrow but the visit of Stoke City to the Emirates Stadium in the Premier League on Saturday will see the onus placed on his regulars to bounce back.

"We have to show our mental strength now," said Rosicky.

"Letting our season fall apart would be the biggest mistake we can make.The next match is vital for us to get back on track. After a defeat like Chelsea, you need to have a good reaction. If not, it could be even more difficult."

The Chelsea striker Didier Drogba believes his side "sent a big message to the teams in England" with the win over Arsenal, in which he scored twice. "We have the team to stay ahead of all the others," said the Ivorian. Chelsea also beat Manchester United, another of their title rivals, last month.

"Our strength is that we are able to switch it on when it matters. Against United it was a really difficult game but we still won it. We know how to go through difficult periods, difficult times ... Against Arsenal, every time we had a chance we took it." Chelsea are confident Ashley Cole will recover from a hamstring strain to face Manchester City on Saturday.